The long-term goals of this proposal are to discover core human conceptions of the world through studies of their origins in infancy, and to chart the role of these core systems in the development of cognitive and social skills. Four sets of experiments focus on human infants' and preschool children's developing sensitivity to and understanding of number. These experiments investigate the emergence and nature of capacities to form abstract numerical representations linking information in different perceptual modalities, to transform numerical representations by the operations of arithmetic, to grasp logical properties of arithmetic such as the inverse relationship between addition and subtraction, and to order arithmetic operations in accord with the syntactic constraints of elementary mathematics. Five sets of experiments focus on children's developing sensitivity to geometry in the larger spatial layout in which they navigate, in three dimensional visual arrays of objects, and in visual forms. These experiments investigate children's capacities to analyze geometric relationships and to link different sources of geometric information as they learn to use maps and measurement devices. Five further sets of experiments focus on children's developing sensitivity to social distinctions among other children and adults based on their language, gender, ethnicity, or behavior. These experiments investigate social category effects on children's choices of social partners, reasoning about social interactions between other children, and preferences between activities and objects endorsed by other children or adults. Three classes of methods are used to assess infants' perceptual and cognitive development in these domains. First, preferential looking and head-turning methods focus on infants' tendency to attend differentially to events, arrays of objects, geometric displays, or people that are novel vs. familiar or mathematically consistent vs. inconsistent. Second, reaching and locomotor search methods focus on infants' and young children's search for objects in spatial arrays and their tendency to accept or offer objects to other individuals. Third, simple verbal questions assess children's mathematical understanding or social preferences. By means of these converging measures, the research aims to elucidate core cognitive systems at the foundation of human knowledge. PUBLIC HEALTH RELEVANCE: The proposed experiments investigate the early development of human knowledge of the immediately surrounding physical and social world. An understanding of numerical, geometrical, and social cognition in infancy and early childhood promises to shed light on the structure and acquisition of knowledge more generally, and to contribute to the detection and treatment of children with developmental disabilities such as deficits in calculation, in spatial reasoning, or in social interaction.